Download one page review of static electricity

ONE PAGE REVIEW OF STATIC ELECTRICITY
 Charge, q: Comes in two forms + and -; opposite charges attractive, same charges repel; measured in units of Coulombs (C)
The only type of charge that can move around is the negative charge, or electrons. The positive charge stays in the nuclei.
So, we can put a NET CHARGE on different objects in two ways
◊ Add electrons and make the object negatively charged.
◊ Remove electrons and make the object positively charged.
 Electrical conductors, insulators, semiconductors and superconductors
-
distinction based on their ability to conduct (transfer between materials) electric charge.
-
Conductors have loosely bound electrons, allows them to conduct heat and electricity.
Examples: human body, metals, tap water
-
Insulators have tightly bound electrons, which makes them poor conductors of heat and electricity.
Examples: rubber, plastic, dry air
-
Semiconductors sometimes act as conductors, sometimes as insulators. Useful as switches. Can easily adjust the amount
of resistance.
Examples: silicon, germanium
-
Superconductors have virtually no resistance, which means they can transmit current with no energy loss.
Examples: metals or ceramics at exceptionally cold temperatures (between 0 – 100 K)
 Polarization occurs when charge becomes separated on a neutral object (one side becomes positively charge, one side becomes
negatively charged). Objects can become polarized if they are brought close to a charged object.
 Electrostatic Force between TWO POINT charges q1 and q2 at distance r from each other is proportional to the product of the
amount of the charges on each one, and inversely proportional to the square of the distance between them.
F k
q1q2
r2
k  8.99 109 N  m 2 / C 2
Force is a vector, therefore it must always have a direction.
 Electric Field is an area around a charge where another charge may feel a force. Symbol: E Units: N/C
The magnitude of the electric field can be measured by the force it exerts on a test charge: E = F / q
Alternatively, the magnitude of the electric field generated by a single charge can be calculated by E = kq/r2
The direction of the magnetic field is the direction of the force on a positive test charge.
We can visualize the electric field around charges by drawing electric field lines. Electric field lines show the direction of net
electric force on a positive charge. Electric field lines can never cross. The strength of the electric field is shown in the density of
the lines; the greater the density of field lines, the stronger the field.
ONE PAGE REVIEW OF CIRCUITS
• length, L
 Resistance of a wire when the temperature is kept constant is:
𝑅=𝜌
𝐿
• cross-sectional area, A
𝐴
• material/resistivity, ρ
 OHM’S LAW: Current through resistor is proportional to potential difference
across the resistor and inversely proportional to resistance
of that resistor.
𝐼 =
𝑉
𝑅
𝐼(𝐴)
𝑉(𝑉)
𝑅(𝛺)
 Electric power, P, is the rate at which energy is supplied to or used by a device in which electric energy is
converted into another form such as mechanical energy, thermal energy, or light.
Power dissipated in a resistor:
P=IV
P=
𝑉2
𝑅
= 𝐼2 𝑅
Power of the source = ε I
Electric energy is: 𝐸 = 𝑃 𝑡
𝑠𝑜
𝐸 (𝐽𝑜𝑢𝑙𝑒𝑠) = 𝑃(𝑊𝑎𝑡𝑡𝑠) × 𝑡(𝑠)
𝐸 (𝑘𝑊ℎ) = 𝑃(𝑘𝑊) × 𝑡(ℎ)
 Electromotive force, 𝜺, is the voltage generated by battery (how much energy per unit charge is available for
the circuit including internal resistance)
Resistors in Series
• connected in such a way that all components have the same current through them.
𝑅𝑒𝑞 = 𝑅1 + 𝑅2 + 𝑅3
𝑉
𝐼=𝑅
𝑒𝑞
Resistors in Parallel
• Electric devices connected in parallel are connected to the same two points of an electric circuit, so all components have the same
potential difference across them.
• The current flowing into the point of splitting is equal to the sum of the currents flowing out at that point:
𝐼 = 𝐼1 + 𝐼2 + 𝐼3
𝑎𝑛𝑑 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑑𝑟𝑜𝑝 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑎𝑐𝑟𝑜𝑠𝑠 𝑎𝑙𝑙 𝑟𝑒𝑠𝑖𝑠𝑡𝑜𝑟𝑠: 𝐼1 𝑅1 = 𝐼2 𝑅2 = 𝐼3 𝑅3
The greater resistance, the smaller current.
1
𝑅𝑒𝑞
=
1
𝑅1
1
1
+𝑅 +𝑅
𝐼=
2
𝑉
𝑅𝑒𝑞
A device that transforms mechanical energy into electrical energy is called a generator.
A device that transforms electrical energy into mechanical energy is called an electric motor.
A transformer is a device that transforms/change voltage.
3
ONE PAGE REVIEW OF MAGNETISM
The direction of a magnetic field line is defined as the direction in which the north pole of a
compass points when it is placed in the magnetic field.
Outside the magnet, the field lines emerge from the magnet at its north pole and enter the
magnet at its south pole.
Inside the magnet, there are no isolated poles on which field lines can start or stop, so
magnetic field lines always travel inside the magnet from the south pole to the north pole to
form closed loops.
Magnetic field is measured in Tesla
1 T(Tesla) =
N∙s
C∙m
1. An electric charge experiences a magnetic force when moving in a magnetic field.
Magnetic force acting on a charge q
Magnetic force on a wire carrying current I
in a magnetic Field B: F = qvB sinin a magnetic field B: F = I LB sin
 
q = charge [C]
I = current [A]
v = velocity [m/s]
L = length [m]
B = magnetic field [Tesla T]
B = magnetic field [T]
 = angle between v and B

 = angle between I and B
R-H-R 1: The direction of the magnetic force on a charge/current is given by the right-hand rule 1:
Outstretch fingers in the direction of v (or current I).
Curl fingers as if rotating vector v (I ) into vector B.
Magnetic force on a positive charge (or I) is in
the direction of the thumb.
Magnetic force on a negative charge points in opposite direction.
2. A moving charge produces a magnetic field.
R-H-R 2: The direction of the magnetic field produced by electric current is given by the right-hand rule 2:
If a wire is grasped in the right hand with the thumb in the direction of current flow, the fingers will curl in the direction of the magnetic
field.
= the permeability of free space 4×10-7 T·m/A
Magnetic field B around a wire with current I B =
𝜇0 𝐼
2𝜋 𝑟
I = current [A]
r = distance from the center of the conductor
ONE PAGE REVIEW OF KINEMATICS
Displacement – A change of position in particular direction. A distance in a given direction. Vector. Unit: meter (m)
total displacement
Average Velocity =
total time
(Instantaneous) Velocity – Value of velocity at a particular time.
Acceleration =
change in velocity
(vector) (m/s2)
time taken for that change
Acceleration can cause:
1. change in speed (speeding up: v and a in the same direction;
slowing down: v and a in the opposite direction)
2. changing direction
3. both
Motion with constant velocity (equal displacements in the equal amounts of time)
x = vt
magnitude of velocity = speed
v avg = v
Motion with constant acceleration a
v = u + at
vavg =
u+v
2
x =
u+v
2
t
x = ut +
𝑎
2
t2
v2 = u2 + 2ax
Free Fall formulas – Formulas are the ones for uniform accelerated motion with a = g
u+v
u+v
g 2
v = u + gt
vavg =
y =
t
y = ut +
t
2
2
2
2
2
g = 9.8 m/s , downward ≈ 10 m/s .
v2 = u2 + 2gy
Remember that in the coordinate system in which upward is chosen to be positive, g is negative and vice versa.
If air resistance is not mention it is assumed that we ignore air resistance.
When the object reaches maximum height, the velocity of the object is 0 m/s, but acceleration is still g = 9.8 m/s2 downward.
Velocity changes, but g does NOT!!!
Terminal speed – When air resistance is taken into account object in free fall will not accelerate forever. The speed of the object will
increase until the object reaches a maximum, constant speed
Graphs for:
motion with constant velocity
positive direction is away from
the initial position
motion with constant acceleration
positive direction is away from
the initial position
free fall (up and down)
positive direction is upward
ONE PAGE REVIEW OF FORCES
Inertia is resistance an object has to a change of velocity
Mass is numerical measure of the inertia of a body / is a measure of the amount of matter in the object unit: kg
• doesn’t depend on the location of the object . Object of mass of 1 kg here on earth would have the mass
of 1 kg on the moon, even though it would weigh only one-sixth as much.
Weight is the gravitational force acting on an object .
• W = mg
unit: Newton (N)
Net force, Fnet, is the vector sum of all forces acting on an object
Free Body Diagram/ Force diagram is a sketch of a body and all forces acting on it.
Newton’s first law: An object continues in motion with constant speed in a straight line (constant velocity)
or at rest unless acted upon by a net external force.
 If net force is zero, acceleration is zero, velocity is constant (or zero).
The object is in equilibrium. Any force acting on it is balanced.
Newton’s second law: If a net force is acting on an object of mass m, object will acquire acceleration proportional to the net force
and inversely proportional to the mass of the object. Direction of acceleration is direction of the net force.
𝑎⃗ =
𝐹⃗𝑛𝑒𝑡
𝑚
Newton’s third law:
Whenever object A exerts a force on object B, object B exerts an equal in magnitude but
opposite in direction force on object A
FA - force object A exerts on object B
We are talking about forces
acting on two different bodies.
FB - force object B exerts on object A
Tension T is a force that the end of the rope exerts on whatever is attached to it.
Direction of tension is along the rope.
Normal force Fn is the force which is preventing an object from falling through the surface of another body .
That’s why normal force is always perpendicular (normal) to the surfaces in contact.
Friction force Ffr is the force that opposes slipping (relative motion ) between two surfaces in contact;
it acts parallel to surface in direction opposed to slipping.
 Friction depends on type and roughness of surfaces and normal force.
Ffr = μ Fn
μ is called coefficient of friction
• μ has no units
• it is a measure of surface-to-surface roughness
• depends on characteristics of both surfaces
• different values for static and kinetic coefficient of friction (tables)
• kinetic μ is smaller than static μ. You probably noticed that once you moved
something from rest it becomes easier to push around.
Newton’s Law of Universal Gravitation: Force between masses m1 and m2 that are at distance r from each other
attract each other with the force
F=G
m1 m2
r2
ONE PAGE REVIEW OF WORK, ENERGY, AND MOMENTUM
Momentum, p is mass times velocity:
p=mv
Impulse F∆t will produce change in momentum Δp:
vector!
unit: (p) = kg m/s
F∆t = ∆p
Δp = mv - mu
Example: You want to throw a ball (m=0.5 kg) over a tree. You hit it at 60o so it leaves your hand at the speed of 10 m/s.
Unfortunately that was not enough. Your ball is now stuck in the tree. It was just at its maximum height. What impulse
did you impart on the ball. What impulse did the tree exert on the ball?
you: impulse = change in momentum = 5 kg m/s.
tree: at the top speed is equal to the horizontal component of the velocity = 10 cos 600 = 5 m/s impulse = change in
momentum = 2.5 kg m/s
Law of conservation of momentum:
In collision
pafter = pbefore
m1v1 + m2v2 = m1u1 + m2u2
WORK and ENERGY (measured in Joules)
Work done by external force changes potential energy (when net force is zero, so there is no acceleration).
Gravitational Potential energy, PE = mgh
What work should be done in raising an object of mass 6 kg to the top of the incline?
W=mgh = 180 J
What (minimal) force should be applied to push it along the incline to the top:
F = mg sin θ = 60 (3/5) = 36 N
Work done by net force changes kinetic energy (net force gives acceleration, therefore changes velocity).
the change in the kinetic energy of the object is equal to the net work done on the object.
W = ∆KE = KEf – KEi = ½ mv2 – ½ mu2
Example: Firework explodes into three pieces of equal mass. They all move in three different directions each with the speed v.
What work was done on firework?
W = ∆KE = 3(½ mv2)
In addition remember that momentum must be conserved !!!!!
Conservation of energy law
For the system that has only mechanical energy (ME = PE + KE)
and there is no frictional force acting on it, so no mechanical energy
is converted into heat, mechanical energy is conserved
ME1 = ME2 = ME3 = ME4
mgh1 + ½ mv12 = mgh2 + ½ mv22 = • • • • • •